Last week, the court published its first full reasoning for one such decision, in which the cross-country skier Alexander Legkov had his punishment overturned because, the court said, it could not be certain the athlete himself had been personally involved in the cheating scheme, in spite of suggestive evidence that his urine sample had been manipulated.

Russian officials have seized on victories like Mr. Legkov’s, calling them a vindication of the nation’s athletes and a repudiation of Dr. Rodchenkov. In recent days, Russian officials have claimed that Dr. Rodchenkov has walked back or retracted his statements about Russia’s cheating.

“We see now as a fact that this person is confused with his testimonies, that he is actually confirming his lies and his slander,” Dmitry Peskov, President Putin’s spokesman, told Russian state media last week.

But Dr. Rodchenkov’s lawyers — Mr. Walden, of Walden Macht & Haran, and Gregory L. Diskant of Patterson Belknap in New York — said their client “had not wavered,” calling him “very clear and very highly corroborated.”

“If the Russians seriously believe there is no state-sponsored doping system, why didn’t they produce the emails, the lab data, the stored samples at the Moscow lab?” Mr. Walden said, referencing certain specific evidence that regulators and investigators have long requested of Russia, which remains decertified by the global antidoping regulator and barred from track and field competitions.

In the filings on Monday, Dr. Rodchenkov responded to the libel claim with a simple defense: He argued he had told the truth, pointing to scientific and forensic evidence that later confirmed much of what he had told The New York Times in 2016.

Dr. Rodchenkov’s countersuit is likely to seek in depositions the names of the others who are financing the lawsuit against him, as well as information on the assets of Mr. Prokhorov, who this spring sold 49 percent of his stake in the Nets but remains the team’s controlling owner.

“Prokhorov has assets here,” Mr. Walden said. “We need to go about expeditiously securing them, so he doesn’t go about taking them out of the country. You can expect that’s what we’re going to be looking at next.”